How to separate animation of materials in Blender Internal?
I've had this problem and found it's best to press the UPPER plus symbol, not the one indicated.  This will create a new material slot accessible to the object selected and one which is independent of those already there.

Back in the 3D window get into edit mode, switch to "Faces" and select those surfaces you wish to allot this new material to.

Go back to the UPPER panel (to the left of the upper plus sign) and make sure the new slot is still highlited.  If it's not, click on it. 

The unnamed material will also appear in the slot next to the lower plus symbol.  Click in there (NOT on the plus sign) and give it a name.

Only when both the desired surfaces (in EDIT MODE) AND the material slot in the upper panel are highlited should you press the "Assign" button a little below.   

The assign button will connect your highlited faces to the new slot.  

You should see those surfaces/faces immediately react and change colour.  

There should be no keyframes in the dopesheet for this new material either.  Any you do create later will only affect the new slot and  those surfaces you've just assigned to it.